Ch. 15--ANOVA

1. Use of flow chart

2. Overview



3. The F test

a. sampling distribution of F



b. F table

c. when to use the F test

i. more than 2 groups





i. F vs. Multiple t-tests

4. Generating Hypotheses for ANOVA



5. Calculating the statistic

a. Conceptual F



i. Total Variance









ii. Between-group variance











iii. Within group variance



iv. Fobt = sb2/ sw2



b. Calculating Fobt

Source of variance SS df s2 (MS) Fobt

Between groups formula k-1 Ssb / dfb sb2/ sw2

Within groups formula N-k Ssw / dfw

Total Formula N-1



SSb =

SSw =

SSt =

Example

is there a difference exam scores as a function of teaching style? 3 different teachers.

X1 X2 X3

52 46 44

57 52 53

55 51 50

59 50 51



6. Evaluating Fobt--compare with fcrit





7. Comparison between F and t

i. testing means

ii. t2 = F

8. Assumptions of ANOVA

i. normal distribution

ii. Homogeneity of variance

iii. Robust

9. Two-way, or Factorial ANOVA

i. Factorial experiment: when two or more factors are assessed

ii. Use a two-way ANOVA

iii. Components to understand:

a. main effects= effect of one IV independent of the other

b. interaction= when the effect of one IV is not the same at all levels of the other IV



iv. F's for main effects

a. IV1 : F = sr2 /sw2

b. IV2 F = sc2 /sw2

c. Interaction: F = src2 /sw2

Statistics